摘要
采用激光跟踪仪测量系统结合视觉测量系统进行相对位姿标定时,最小二乘算法(LS)由于未顾及函数模型中系数矩阵元素存在的随机误差,将降低相对位姿参数的求解精度.因此,基于罗德里格矩阵的坐标转换模型,引入部分变量误差模型(PEIV)加权总体最小二乘(WTLS)算法求解位姿标定参数.为减免粗差的影响,利用具有高崩溃污染率的中位数抗差方法计算单位权中误差,并对残差进行标准化处理,选取Danish函数作为等价权函数,对观测值和系数矩阵元素进行合理赋权.实例分析结果表明,应用该方法进行标定,在某点坐标分量存在 0.05 mm粗差情况下,最大可减少 0.04 mm的单位权中误差,根据标定参数计算的坐标值较LS更接近理论值,证实本文方法的有效性.
Abstract
As the laser tracker measurement system combines the visual measurement system to perform the relative position and pose calibration,the least-squares algorithm(least-squares,LS)will reduce the solution accuracy of the relative position and pose param-eters due to the ignorance of random errors of the coefficient matrix element in the function model.Therefore,the coordinate transfor-mation model based on the Lodrigues matrix introduces a partial errors-in-variables(PEIV)weighted total least-squares(WTLS)al-gorithm to solve the relative position and pose parameters.To reduce the impact of gross error,the median robust method with a high crash pollution rate is used to calculate the error in the unit weight and standardize the residuals,and the Danish function is selected as the equivalence weight function to reasonably weight the observed values and coefficient matrix elements.The experimental results show that the application of this method of relative position and pose calibration reduces the error in the unit weight by 0.04 mm at the maximum in the case of a gross error of 0.05 mm in the coordinate components of a certain point,and the coordinate values calculated according to the calibration parameters are closer to the theoretical values than LS,which proves the effectiveness of the proposed method.
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